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09/06/2023
A General Approach to Proving Properties of Fibonacci Representations via Automata Theory
We provide a method, based on automata theory, to mechanically prove the...
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08/12/2023
Proving properties of some greedily-defined integer recurrences via automata theory
Venkatachala on the one hand, and Avdispahić Zejnulahi on the other,...
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05/04/2023
Proving Properties of φ-Representations with the Walnut Theorem-Prover
We revisit a classic theorem of Frougny and Sakarovitch concerning autom...
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03/27/2023
Transduction of Automatic Sequences and Applications
We consider the implementation of the transduction of automatic sequence...
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02/25/2023
Smallest and Largest Block Palindrome Factorizations
A palindrome is a word that reads the same forwards and backwards. A blo...
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02/09/2023
Prefixes of the Fibonacci word
Mignosi, Restivo, and Salemi (1998) proved that for all ϵ > 0 there exis...
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02/01/2023
Rudin-Shapiro Sums Via Automata Theory and Logic
We show how to obtain, via a unified framework provided by logic and aut...
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01/27/2023
Proof of a conjecture of Krawchuk and Rampersad
We prove a 2018 conjecture of Krawchuk and Rampersad on the extremal beh...
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01/15/2023
Dyck Words, Pattern Avoidance, and Automatic Sequences
We study various aspects of Dyck words appearing in binary sequences, wh...
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12/23/2022
Counterexamples to a Conjecture of Dombi in Additive Number Theory
We disprove a 2002 conjecture of Dombi from additive number theory. More...
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10/08/2022
Some Tribonacci Conjectures
In a recent talk of Robbert Fokkink, some conjectures related to the inf...
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09/20/2022
Complement Avoidance in Binary Words
The complement x of a binary word x is obtained by changing each 0 in x ...
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09/19/2022
Antisquares and Critical Exponents
The complement x̅ of a binary word x is obtained by changing each 0 in x...
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08/11/2022
Automatic Sequences in Negative Bases and Proofs of Some Conjectures of Shevelev
We discuss the use of negative bases in automatic sequences. Recently th...
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07/20/2022
Pseudoperiodic Words and a Question of Shevelev
We generalize the familiar notion of periodicity in sequences to a new k...
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06/03/2022
Properties of a Ternary Infinite Word
We study the properties of the ternary infinite word p = 012102101021012...
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03/20/2022
Note on a Fibonacci Parity Sequence
Let ftm = 0111010010001... be the analogue of the Thue-Morse sequence in...
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03/06/2022
Intertwining of Complementary Thue-Morse Factors
We consider the positions of occurrences of a factor x and its binary co...
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12/22/2021
Properties of a Class of Toeplitz Words
We study the properties of the uncountable set of Stewart words. These a...
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08/11/2021
Automatic Sequences of Rank Two
Given a right-infinite word x over a finite alphabet A, the rank of x is...
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07/29/2021
Mesosome Avoidance
We consider avoiding mesosomes – that is, words of the form xx' with x' ...
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06/02/2021
Hilbert's spacefilling curve described by automatic, regular, and synchronized sequences
We describe Hilbert's spacefilling curve in several different ways: as a...
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03/19/2021
Frobenius Numbers and Automatic Sequences
The Frobenius number g(S) of a set S of non-negative integers with 1 is ...
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02/16/2021
Decidability for Sturmian words
We show that the first-order theory of Sturmian words over Presburger ar...
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02/07/2021
Lie complexity of words
Given a finite alphabet Σ and a right-infinite word w over Σ, we define ...
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12/12/2020
String Attractors for Automatic Sequences
We show that it is decidable, given an automatic sequence s and a consta...
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11/01/2020
Abelian Complexity and Synchronization
We present a general method for computing the abelian complexity ρ^ ab_ ...
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10/21/2020
Subword complexity of the Fibonacci-Thue-Morse sequence: the proof of Dekking's conjecture
Recently Dekking conjectured the form of the subword complexity function...
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08/03/2020
The Largest Entry in the Inverse of a Vandermonde Matrix
We investigate the size of the largest entry (in absolute value) in the ...
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07/29/2020
Robbins and Ardila meet Berstel
In 1996, Neville Robbins proved the amazing fact that the coefficient of...
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07/16/2020
The Simplest Binary Word with Only Three Squares
We re-examine previous constructions of infinite binary words containing...
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06/17/2020
Extremal overlap-free and extremal β-free binary words
An overlap-free (or β-free) word w over a fixed alphabet Σ is extremal i...
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06/07/2020
Sumsets of Wythoff Sequences, Fibonacci Representation, and Beyond
Let α = (1+√(5))/2 and define the lower and upper Wythoff sequences by a...
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05/24/2020
An inequality for the number of periods in a word
We prove an inequality for the number of periods in a word x in terms of...
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05/19/2020
A Frameless 2-Coloring of the Plane Lattice
A picture frame in two dimensions is a rectangular array of symbols, wit...
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05/19/2020
Decidability and k-Regular Sequences
In this paper we consider a number of natural decision problems involvin...
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02/07/2020
Computational Aspects of Sturdy and Flimsy Numbers
Following Stolarsky, we say that a natural number n is flimsy in base b ...
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02/05/2020
Avoidance of split overlaps
We generalize Axel Thue's familiar definition of overlaps in words, and ...
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12/17/2019
New Bounds on Antipowers in Binary Words
Fici et al. defined a word to be a k-power if it is the concatenation of...
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11/27/2019
Words With Few Palindromes, Revisited
In 2013, Fici and Zamboni proved a number of theorems about finite and i...
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11/26/2019
Words Avoiding Reversed Factors, Revisited
In 2005, Rampersad and the second author proved a number of theorems abo...
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06/09/2019
Borders, Palindrome Prefixes, and Square Prefixes
We show that the number of length-n words over a k-letter alphabet havin...
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04/19/2019
New results on pseudosquare avoidance
We start by considering binary words containing the minimum possible num...
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04/17/2019
Circularly squarefree words and unbordered conjugates: a new approach
Using a new approach based on automatic sequences, logic, and a decision...
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03/13/2019
Generalized de Bruijn words and the state complexity of conjugate sets
We consider a certain natural generalization of de Bruijn words, and use...
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02/01/2019
Critical exponent of infinite balanced words via the Pell number system
In a recent paper of Rampersad et al., the authors conjectured that the ...
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08/07/2018
Circular critical exponents for Thue-Morse factors
We prove various results about the largest exponent of a repetition in a...
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02/13/2018
Lengths of Words Accepted by Nondeterministic Finite Automata
We consider two natural problems about nondeterministic finite automata....
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01/25/2018
Rollercoasters and Caterpillars
A rollercoaster is a sequence of real numbers for which every maximal co...
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01/16/2018